07A-38

[kevinp94]

On a Texas ranch, a pond is 285 ft in diameter and the land slopes at 4 degrees (from horizontal) away from the pond. What is the pond diameter after a 1.5 in rain if 40% of the rain runs into the pond, and the rain gathering area is 3 acres? (answer in ft)

I've drawn out this problem and thought a lot about it. I surmise that the resulting water increase would be in a frustum. I was trying to find the height of the frustum in order to work backwards and find the new diameter, but I can't seem to find a way. (tried using similar triangles, trig with the 4 degrees) no luck

Could anybody give me another way of thinking or post a solution to this problem? I would greatly appreciate it because I am studying for an upcoming tournament. Thank you!

[bradp]

its a cone actually

Find the original volume using the original diameter to find radius and height (get height with trig). Add the volume of the additional rain. Reverse the volume process to find new diameter

[AuSmith]

Here's an alternate solution. Brad's way is simpler.

The rain water that ends in the pond has volume [unparseable or potentially dangerous latex formula] and is in the shape of a frustum (with small radius [unparseable or potentially dangerous latex formula]). Maybe you should convert everything to feet.

[unparseable or potentially dangerous latex formula]

You can relate the height of the frustum to the larger radius:

[unparseable or potentially dangerous latex formula]

Then, use the second equation to solve for [unparseable or potentially dangerous latex formula] and substitute it into the first.

[unparseable or potentially dangerous latex formula][unparseable or potentially dangerous latex formula]

Sub in [unparseable or potentially dangerous latex formula] and whatever [unparseable or potentially dangerous latex formula] is.